FWIW, for me, this is an anti-feature, and I would not use this language because of it. The net effect of this would be that I type "mutable" all over the place and get very little for my effort.
I've spent a significant amount of time understanding what the high-consequence programming errors that I make are, and "oops, I mutated that thing that I could have marked const" is a class of error that consumes a vanishingly small amount of my debugging time.
The errors I make that account for a large portion of my debugging time are errors related to semantics of my program. Things that, in C++, are typically only detectable at runtime, but with a better type system could be detected at compile time. The first step for this might be type annotations that specify valid values. For example, being able to annotate whether an argument is or is not allowed to be null, and having that enforced at call sites.
(NOTE: I also don't spend a meaningful amount of time debugging accidental nullptr values, but that's a good first step towards the type annotations I _do_ want)